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'Snail Trails' printed from http://nrich.maths.org/

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This is a game for two players. You will need some small-square grid paper, a die and two felt-tip pens or highlighters.

  1. Mark a starting point and a target square.
  2. Players take turns to roll the die, then move that number of squares in a straight line.
  3. Move only vertically (up/down) or horizontally (across), never diagonally.
  4. You can cross over the other player's trails. You can trace over the top of the other player's trails.
  5. You can cross over a single trail of your own, but can never cross a pair of your trails (side-by-side) or trace over your own trail.
  6. To win, you must roll the exact number needed to finish in the target square. You can never pass through the target square.
  7. The game ends when a player ends his/her trail in the target square, OR when a player cannot move without breaking any of the rules.
Grid

Does it matter where the target is put? Is there a good strategy for winning? If you could choose your own numbers, what would be the shortest possible trail?